Periodic potential-energy landscapes have exceptional promise for sorting continuous streams of mesoscopic objects. Whether an object becomes locked in to a symmetry-selected direction through the landscape or instead follows the direction of the driving force can depend sensitively on size. This can be shown quite generally for the separable potentials considered in Secs. 4 and 5. More subtle landscapes, which involve coupled motions in two or more dimensions, are more difficult to analyze. Approximate arguments and simulations show that a particular one of these, a line of Gaussian wells, offers both exponential size selectivity and clean binary separations. More sophisticated, non-separable, higher-dimensional landscapes, such as two-dimensional arrays of optical traps (4), optical lattices (5), and microfabricated post arrays (3,2), can distribute continuous distributions of objects into discrete fractions (28). The analysis in this case is made far more difficult by the lack of closed-form solutions to the equations of motion, even in the deterministic limit.
Randomization by thermal forces substantially degrades the selectivity with which a one-dimensionally modulated landscape can retain objects. A related study demonstrates that thermal forcing restructures the pattern locked-in states in a two-dimensional array of potential wells (28), and eventually wipes them out as the array grows in size. This contradicts the assertion (5) that thermally assisted hopping can lead to exponential size selectivity. Fortunately, the sorting processes discussed here, as well as their generalizations, can be driven into the deterministic limit by increasing the driving and trapping forces.
Continuous, continuously tuned chromatographic size separations should have many applications in biological research, drug discovery, and purification of mesoscale materials. This Article outlines the basic principles by which they work, and suggests considerations for their optimization for particular applications.
This work was supported by the National Science Foundation under Grant Number DBI-0233971 and Grant Number DMR-0304906.